For a design of deviated well trajectory, it is important to estimate torque and drag and to select the most appropriate well trajectory. Some equations of torque and drag have been proposed under an assumption that torque and drag forces are primarily caused by sliding friction. However, since they are formulated as an incremental equation using short element of the pipe, they have a little short versatility, i.e., necessity of computer usage. Under an assumption that azimuth angle and inclination angle do not change together over a bending section, the incremental equation can be transformed to differential equations. Based on conducted differential equations for three bending sections, theoretical formulas for inclination angle change section and approximate formula for azimuth angle change section are both derived as algebraic equation. These formulas can easily calculate torque and drag using only bending condition parameters. It is found that the proposed formulas can be used as a convenient estimating method, since the estimate for hookload including drag agrees well with one obtained by conventional iteration of the incremental equation.
For an extended reach drilling simulation, many important techniques arerequired. Torque and drag prediction is one of them. There is an opinion that catenary trajectorycan minimize drag. However, as drag is accumulated upward, drag is affected not only by bendingrate but by hook load and inclination angle at lower end of catenary. For a temporary evaluationwhether drag of catenary is the minimum or not, two types of trajectory are compared throughsimulation study. One is an approximate catenary trajectory which composed of multiple build upsection with different bending rate, and another is equivalent build up section which has the sameinclination angle and lower end as the former. The following findings are obtained.(1) Drag of approximate catenary trajectory does not remarkably decrease comparing with thatof equivalent build up section.(2) When drag of catenary trajectory decreases comparing original build up section, the majordecrease of drag may be contributed to the connecting downward tangent section.(3) In this sense, the effect of catenary for drag decrease may be said that catenary can increaseinclination angle, since high inclination angle can decrease drag over downward tangentsection.
